early 14c., "slender, edible marine crustacean," probably from Old Norse skreppa "thin person," from Proto-Germanic *skrimp- (see scrimp). Related to Old English scrimman "to shrink;" the connecting notion is probably "thinness" (compare Danish dialectal skrimpe "thin cattle"). The meaning "puny person" in English is attested from late 14c.; an especially puny one might be a shrimplet (1680s).
"fish for shrimp," 1801 (implied in shrimping ), from shrimp (n.). Related: Shrimper (1808).